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Experiment 2

Week 2. (1 Week) Gas Laws CHEM 112 October 4th, 2019 Abigail Brown, 20154053 Derek Esau

Experiment 2

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Name: Abigail Brown

Partner: Erica Smith

Student No: 20154053

Student No: 20162183

Lab Section: 10

Bench #: 10

Experiment 2: (1 week) (GAS) Gas Laws Purpose The purpose of this lab was to familiarize ourselves with the gas laws by testing how pressure, volume, temperature, and amount (in moles) relate [1]. Introduction Boyle’s Law is named after physicist Robert Boyle, who published the original law in 1662. Boyle’s Law states that there is an inverse relationship between pressure and volume of a gas, only if temperature and amount in moles are kept constant [2]. Boyle’s Law can be modelled by the equation P1V1=P2V2, where P1 is the initial pressure, V 1 is the initial volume, P2 is the final pressure, and V 2 is the final volume. Gay-Lussac’s Law is named after the French chemist Joseph Gay-Lussac. Gay-Lussac discovered the relationship between pressure and temperature. Gay-Lussac’s Law states that the pressure of a given mass of gas varies

directly with the absolute temperature of the gas, when the volume is kept constant [3]. This P1 P2 = relationship can be modelled by the equation , where P1 is the initial pressure, T1 is the T1 T 2 initial temperature, P2 is the final pressure, and T2 is the final temperature. Note that temperature must be measured in Kelvins and not Celsius. In the early 1800s John Dalton discovered the relationship between pressure and amount of a gas, the subsequent law was named after him. Dalton’s Law states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the gases in the mixture [4]. An equation to represent Dalton’s Law is: PA=PtotalxA, where xA is the mole fraction for the Ath component of the mixture, and PA is the partial pressure for the Ath component. Finally, the ideal gas law is a law to show how volume(V), pressure(P), and temperature(T) of an ideal gas are related [5]. The relationship is modelled by the equation PV=nRT, where n is the amount in moles and R is the gas constant.

Procedure [1] Part 1 1. Open Logger Pro on the computer and set up a graph that has pressure (atm) on the y-axis and volume (mL) on the x-axis. 2. Prepare the syringe for data collection by moving the piston to the 10.0 mL mark. Then attach the syringe to the pressure sensor. 3. Select the [Collect] setting on Logger Pro and collect data for the volume and pressure at 5.0, 7.5, 10.0, 12.5, 15.0, 17.5, and 20.0 mL. The volume can be changed by moving the piston and lining up the inner black ring with the marking for the desired volume. Make sure to record the pressure and volume data for each trial.

Experiment 2

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4. After collecting the data select a curve of best fit for the graph. Take a screenshot of the graph and save it to One Drive for later access. Part 2 1. Set up a new graph in Logger Pro where pressure (atm) is on the y-axis and temperature (°C) is on the x-axis. 2. Prepare a rubber-stopper flask assembly. To do this, tightly insert the pointy plastic tips into the two openings on the rubber stopper. Insert the rubber stopper into the 125 mL Erlenmeyer flask and then connect the pressure sensor to one of the plastic tips in the rubber stopper and attach the valve switch to the other one. 3. Begin collecting the data for a pressure vs. temperature graph on Logger Pro. Collect the data at the four temperature points: ice bath, room temperature bath, hot water bath, and boiling water bath. Use tongs to transfer the flask between the various temperature points. Record the pressure and temperature data for each trial. 4. After collecting the data select a curve of best fit for the graph with the temperature scale in Kelvins and one in Celsius. Take a screenshot of the graph and save it to One Drive for later access. Part 3 1. Set up Logger Pro to measure the pressure in atm and the temperature in degrees Celsius. 2. Measure out approximately 0.10g of sodium bicarbonate and put it into a clean Erlenmeyer flask. Record the exact mass used. 3. Put the rubber stopper in the flask and attach the pressure sensor to one of the plastic tips. Place the flask and the temperature probe into the room temperature bath. Record the initial pressure and temperature. 4. Dispense about 40mL of 1M of acetic acid into a syringe. 5. Inject the acid into the flask and then pull the plunger back to its original position so as not to change the volume. Gently swirl the flask until the pressure stabilizes and then record the new pressure and temperature. 6. Measure the exact volume of the flask by filling it to the brim with water and using a volumetric flask to determine the exact volume. 7. Clean up. Questions Part 1 1. Based on your data, what would you expect the pressure to be if the volume of the syringe was increased to 40.0 mL? Explain or show work to support your answer. If the volume of the syringe is increased from 10.0mL to 40.0mL then we would expect the pressure to be reduced by a factor of 4.

Experiment 2

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P1V1=P2V2 P2= [(1.0216 atm)(10.0 mL)]/ (40.0 mL) = 0.2554 atm 1.0216/4= 0.2554 Therefore, if the volume is increased to 40.0mL we would expect the pressure to be 0.2554atm. 2. Find the proportionality constant, k, from the data. If this relationship is direct P=kV, then k = P/V. If it is inverse P=k/V, then k = P×V. Based on your data, Calculate k for both equations and then indicate which formula gives the answer that is “constant” for all your P,V data pairs. Choose the correct one of these formulas and calculate the average k value for the seven ordered pairs in your data table (divide or multiply the P and V values). Calculate is the uncertainty, i.e. standard error, in this final mean value of k? (Use statistics; see the section on determining this in the introduction part of the lab manual) There’s an inverse relationship between pressure and volume; therefore, the proportionality constant can be calculated using k=PV. The experimental value of k is 10.45 +/- 0.2787 k= [(9.286)+(9.60225)+(10.216)+(10.69875)+(10.7415)+(11.19825)+(11.436)]/7 =10.45 Standard Error x=10.45 σx=0.7374799617 σmean= (0.7374799617)/(7)1/2

= 0.2787 Part 2 1. In order to perform this experiment, what two experimental factors were kept constant? The volume of the flask, and the amount of moles of gas in the flask were kept constant. 2. Write an equation to express the relationship between pressure and temperature (K). Use the symbols P, T, and k. We know that PV=nRT and in this equation we can assume that volume(V), moles (n), and R are constant, so we can replace them with the variable k. The relationship can be represented by the equation k=P/T 3. Find the proportionality constant k. Like above, if the relationship is direct, k = P/T. If it is inverse, k = PxT. Based on your answer to Question 2, choose one of these formulas and calculate k for the four ordered pairs in your data table (divide or multiply the P and T values). Show the answer in the fourth column of the Part 2 data table. How “constant” were your values?

Experiment 2

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On the data sheet the calculated k values can be found. The k values are not entirely constant as there is a little deviation between the values produced. The values have a range of +/1.2488x10-4. This range in the constant could be related to an experimental error like an unnoticeable leak in seal of the flask. 4. The data that you have collected can also be used to determine the value for absolute zero on the Celsius temperature scale. On the plot of Celsius temperature on the y-axis and pressure on the x-axis, find absolute zero. According to the data we collected, the value for absolute zero is the y-intercept on our graph. This means the experimental value for absolute zero would be -236.4 +/-47.50 degrees Celsius. 5. Since “absolute zero” is the temperature at which the pressure theoretically becomes equal to zero, the temperature where the regression line (the extension of the temperature-pressure curve) intersects the y-axis (b in the y=mx+b equation) should be the Celsius temperature value for absolute zero. What is your experimental value for absolute zero? What is the uncertainty (do a visual estimate based on your plot)? Is your answer correct, i.e. does the real value lie within the limits of your experimental uncertainty? On our graph the value we got for absolute zero was -236.4 +/- 47.50 degrees Celsius. The actual value for absolute zero is -273.15 degrees Celsius, and this real value does lie within the limits of our experimental uncertainty.

Part 3 1. Complete the data sheet and show all calculations in your notebook. Initial Amount of CO2: n=PV/RT n=[(1.0210atm)(0.1570L)]/[(0.08206 L *atm*K-1*mol-1)(295.85K)] n=6.602711298x10-3 mol Final Amount of CO2: n=PV/RT n=[(1.1152atm)(0.1570L)]/( 0.08206 L *atm*K-1*mol-1)(295.75K)] n=7.214332378x10-3 mol Amount of CO2 Added: nadded= nfinal - ninitial =(7.214332378x10-3 mol) – (6.602711298x10-3 mol) =6.116210805x10-4 mol 2. Use Dalton’s law to determine the partial pressure of the CO2 formed. We know the final pressure and the initial pressure of the system and we know that the difference between the two is the contribution of the partial pressure by CO2. Ptotal= P1+P2

Experiment 2

P2= Ptotal-P1 P2= (1.1152 atm)-(1.0210 atm) P2= 0.0942atm 3. Based on the known values: partial pressure (pressure change seen during the reaction), the volume of the flask, the number of moles of CO2 (found using mass of sample and molar mass of NaHCO3) and the final temperature in Kelvin (conversion: T in Celsius + 273.15) what is the value of the gas constant R? – Don’t forget units. Use PV=nRT and solve for R. Determine the uncertainty in R. R= PV/nT R=[(0.0942 atm (101.325kPa/1atm))(0.157L)]/ [(295.75K)(6.12x10-4mol) R=8.28 J/K*mol +/- 0.1 J/K*mol 4. Compare this value to the accepted value. (8.3145 J K-1 mol-1). In this context, compare means that you should determine if the literature value for R agrees with your experimental value within your limits of uncertainty. The literature value for R agrees with our experimental value within the limits of uncertainty.

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Experiment 2

DATA SHEET Part 1 Volume (mL)

Pressure (atm)

Constant, k

P•V

P/ V

5.0

1.8572

9.286

371.44

7.5

1.2803

9.60225

170.707

10.0

1.0216

10.216

102.16

12.5

0.8559

10.69875

68.472

15.0

0.7161

10.7415

47.74

17.5

0.6399

11.19825

36.5657

20.0

0.5718

11.436

28.59

Experiment 2

Part 2 Water Bath

Pressure (atm)

Temperature (°C)

Temperature (K)

Constant, k (P / T or P•T)

1.0210

98.2

371.3

2.749798007x10-3

0.9096

43.0

316.1

2.877570389x10-3

0.8062

24.1

297.3

2.711738984x10-3

0.7681

14.3

287.5

2.671652174x10-3

Boiling Hot Room temp Ice Part 3 Mass of NaHCO3 Volume of flask

Temperature (initial) Temperature (final)

0.170g 157.0mL 22.7˚C 22.6˚C

Pressure (initial) 1.0210atm Pressure (final) 1.1152atm Amount of gas initially in flask Amount of CO2 added

6.60x10-3mol 6.12x10-4 mol

Experiment 2

References 1.

Pages 47-58 of the CHEM 112 Lab Manual.

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Boyle’s Law: Volume and Pressure https://courses.lumenlearning.com/introchem/chapter/boyles-law-volume-andpressure/ Gay-Lussac’s Law https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Book %3A_Introductory_Chemistry_(CK12)/14%3A_The_Behavior_of_Gases/14.05%3A_Gay-Lussac's_Law Dalton’s Law (Law of Partial Pressure) https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbo ok_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Physical_P roperties_of_Matter/States_of_Matter/Properties_of_Gases/Gas_Laws/Dalton's_Law _(Law_of_Partial_Pressures) The Ideal Gas Law https://www.khanacademy.org/science/physics/thermodynamics/temp-kinetic-theoryideal-gas-law/a/what-is-the-ideal-gas-law

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